A block of mass m sits on the top of a block of mass 2 m which sits on a table. The coefficient of kinetic friction between all surface is μ = 1 . A massless string is connected to each mass and wraps halfway around a massless pulley, as shown. Assume that you pull on the pulley with a force of 6 m g . The acceleration of your hand is -

Step-by-step solution

The free body diagrams are : F 1 is force of friction between blocks F 2 is force of friction between block and ground Making FBD of pulley Since pulley is light T = F 2 = 3 mg Let blocks move together with common acceleration a a = 6 m g - F 2 3 m = 6 m g - 3 m g 3 m = g then for upper block T - F 1 = m a ⇒ 3 m g - F 1 = m g ⇒ F 1 = 2 m g but F 1 should be less than f max = μ m g So, our assumption of no relative motion b/w blocks is incorrect that means there is relative motion ⇒   &#1